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4 years ago

10

Consider a vortex filament of strength in the shape of a closed circular loop of radius R. Obtain an expression for the velocity

induced at the center of the loop in terms of T and R

1 answer:

zysi [14]4 years ago

3 0

Answer:

<em>v</em><em> </em>= T/(2R)

Explanation:

Given

R = radius

T = strength

From Biot - Savart Law

d<em>v</em> = (T/4π)* (d<em>l</em> x <em>r</em>)/r³

Velocity induced at center

<em>v </em>= ∫ (T/4π)* (d<em>l</em> x <em>r</em>)/r³

⇒ <em>v </em>= ∫ (T/4π)* (d<em>l</em> x <em>R</em>)/R³ (<em>k</em>) <em>k</em><em>:</em> unit vector perpendicular to plane of loop

⇒ <em>v </em>= (T/4π)(1/R²) ∫ dl

If l ∈ (0, 2πR)

⇒ <em>v </em>= (T/4π)(1/R²)(2πR) (<em>k</em>) ⇒ <em>v </em>= T/(2R) (<em>k</em>)

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Answer:

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Explanation:

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Answer:

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3 years ago

Read 2 more answers

What is the activation energy (Q) for a vacancy formation if 10 moles of a metal have 2.3 X 10^13 vacancies at 425°C?

Yakvenalex [24]

Answer:

$Activation\ Energy=2.5\times 10^{-19}\ J$

Explanation:

Using the expression shown below as:

$N_v=N\times e^{-\frac {Q_v}{k\times T}$

Where,

$N_v$ is the number of vacancies

N is the number of defective sites

k is Boltzmann's constant = $1.38\times 10^{-23}\ J/K$

${Q_v}$ is the activation energy

T is the temperature

Given that:

$N_v=2.3\times 10^{13}$

N = 10 moles

1 mole = $6.023\times 10^{23}$

So,

N = $10\times 6.023\times 10^{23}=6.023\times 10^{24}$

Temperature = 425°C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15

So,

T = (425 + 273.15) K = 698.15 K

T = 698.15 K

Applying the values as:

$2.3\times 10^{13}=6.023\times 10^{24}\times e^{-\frac {Q_v}{1.38\times 10^{-23}\times 698.15}$

$ln[\frac {2.3}{6.023}\times 10^{-11}]=-\frac {Q_v}{1.38\times 10^{-23}\times 698.15}$

$Q_v=2.5\times 10^{-19}\ J$

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3 years ago

In order to fill a tank of 1000 liter volume to a pressure of 10 atm at 298K, an 11.5Kg of the gas is required. How many moles o

lesya [120]

Answer:

The molecular weight will be "28.12 g/mol".

Explanation:

The given values are:

Pressure,

P = 10 atm

= $10\times 101325 \ Pa$

= $1013250 \ Pa$

Temperature,

T = 298 K

Mass,

m = 11.5 Kg

Volume,

V = 1000 r

= $1 \ m^3$

R = 8.3145 J/mol K

Now,

By using the ideal gas law, we get

⇒ $PV=nRT$

o,

⇒ $n=\frac{PV}{RT}$

By substituting the values, we get

$=\frac{1013250\times 1}{8.3145\times 298}$

$=408.94 \ moles$

As we know,

⇒ $Moles(n)=\frac{Mass(m)}{Molecular \ weight(MW)}$

or,

⇒ $MW=\frac{m}{n}$

$=\frac{11.5}{408.94}$

$=0.02812 \ Kg/mol$

$=28.12 \ g/mol$

3 0

3 years ago

How can we calculate the speed of the output gear in a simple gear train? Explain with the help of an example.

Snowcat [4.5K]

Answer:

$N_3=\dfrac{T_1}{T_3}N_1$

Explanation:

In the diagram there three gears in which gear 1 is input gear ,gear 2 is idle gear and gear 3 is out put gear.

Lets take

$Speed\ of\ gear 1=N_1$

$Number\ of\ teeth\ of\ gear 1=T_1$

$Speed\ of\ gear 3=N_3$

$Number\ of\ teeth\ of\ gear 3=T_3$

All external matting gears will rotates in opposite direction with respect to each other.

So the speed of gear third can be given as follows

$\dfrac{T_1}{T_3}=\dfrac{N_3}{N_1}$

$N_3=\dfrac{T_1}{T_3}N_1$

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4 years ago